At home materials Reception Weeks 7—10 Depth of numbers ... · Reception Weeks 7—10 Depth of numbers within 20 Using the at home materials This pack contains seven activities

At home materials

Reception Weeks 7—10

Depth of numbers within 20

Using the at home materials

This pack contains seven activities to develop depth of understanding of numbers within

20.

Each day choose one of the activities to work on with your child, the activities do not need

to be completed in order and you may want to play some of the games/activities more

than once.

Many of the ideas and activities included require more than one player and therefore

participation with an adult or sibling. Provide lots of opportunities to get children to

use mathematical vocabulary and explain their reasoning and reveal their thinking.

Printable resources can be

found at the back of the

pack.

Key Learning

Activity 1: To explore numbers, strategy and patterns within ten

Activity 2: To explore conservation of numbers

Activity 3: To apply knowledge of addition, subtraction and doubles

Activity 4: To apply knowledge of number, shape and measures in their surrounding

environment.

Activity 5: To practise counting forwards and backwards from a number

Activity 6: To explore different ways of making ten

Activity 7: To recognise and extend a pattern

Copyright © 2020 Mathematics Mastery. This can be printed out and photocopied by Mathematics Mastery toolkit registered users only. For further

information please see our terms and conditions at www.mathematicsmastery.org/terms-and-conditions.

Success for all

At school we believe all pupils can achieve success in maths. We encourage pupils

to have a belief that effort leads to success and that challenges are opportunities to

learn.

Here are a few tips to encourage your children at home with maths:

Talk to your children about everyday maths

Play games with them

Value mistakes as learning opportunities

Recognise that there is more than one way to work things out

Praise children for effort over outcome

Avoid saying things like “I’m useless at maths”

Mathematics Mastery

What is ‘Mastery’?

The ‘mastery approach’ to teaching mathematics is the underlying principle of

Mathematics Mastery. Instead of learning mathematical procedures by rote, we want

your child to build a deep understanding of concepts which will enable them to apply

their learning in different situations. To achieve this we aim to develop Conceptual

Understanding, Mathematical Thinking and Language and Communication (see

diagram).

http://www.mathematicsmastery.org/terms-and-conditions



Activity 1: Take down the wall

Key learning: To explore numbers, strategy and patterns within ten

Key vocabulary: One, two, first, second

Important aspects to draw attention to: When there are three bricks left on the wall, ask your child to think about what the other person might do

next if they remove one/two bricks. Give your child fewer bricks to start with (six perhaps) so they can focus on the strategy of how to win.

Encourage your child to record how many they are taking away each time. Can they see a pattern? Repeat the game several times and draw attention to who went first and how many they

took away. Encourage your child to notice if a pattern emerges. Use different coloured bricks for a specific number of remaining bricks (either the last four

or the last three) so that it is easier for your child to notice a key number in deciding who will win.

Provide a recording chart (e.g. on a whiteboard) that shows how many bricks your child and their partner removed on each go so that this can be considered and discussed to identify ‘why’ (incorporating both of the last two points already in there)

Allow your child to explain their own thinking to allow connections to be made between this and the representations used. Likely misconceptions related to this learning:

Children may find it challenging to think of the steps they are making and retain what their partner did. Fewer bricks on the wall would support them. Children may think their choice between 1 and 2 doesn’t matter; winning is determined by who goes first; and/or there is no particular strategy that supports winning

Suggested key questions and opportunities for reasoning

Problem solving and developing mathematical thinking Does the strategy still work if I build the wall instead of taking it down? What if I could take three or four bricks off at a time - would the strategy be the same?

? At what point did you realise you would win/lose the game?

? When there are three bricks left and it is my turn next, can I win? How do you know?

? How can you ensure that you will always win?

? What happens if there are four bricks left and it is your turn, can you win?

Activity overview This activity is based on an ancient strategy game called Nim. At this stage in the year, your child should

be confident with the numbers one and two and so there is much scope within this activity for them to develop their

mathematical thinking within ten, by making predictions and generalising. In this activity you will need to take down the

wall by removing one or two bricks at a time. The winner is the person who takes off the last brick.

Note: to win at this game, you want to ensure it is your opponents turn when there are three bricks left. The strategy can be worked back from this to pinpoint key numbers. Resources: A wall template sheet, ten counters or paper bricks (included)

Suggested sentence structures: “I will take one/two bricks off.” “I think I can win if I go first/second because...”




Activity 2: Equal and unequal sharing

Key learning: To explore conservation of numbers

Key vocabulary:

Number names 0-15, group, share,

equal, unequal, odd, even

Important aspects to draw attention to:

Encourage your child to look for a connection between the number of people, houses and if

they can be shared equally.

Encourage your child to notice that when the number of people in one house decreases, then the number

of people in another house will increase. The total number will remain unchanged.

Encourage your child to begin exploration of odd and even numbers: having an odd number of people to

share when each house needs two people - can you share everyone equally? Why not? Introduce this

vocabulary and use it in the correct context.

Allow your child to explain their own thinking to allow connections to be made between this and the representations

used.

Likely misconceptions related to this learning:

Some children may find it challenging to see the relationship between the number of people in each

house - specifically modelling this using accurate vocabulary may be required.


Problem solving and developing mathematical thinking

Encourage your child to work systematically to find all possible solutions for sharing, equally

and unequally.

? There are nine people and

four houses. Each house

has two people. Does this

work? Why/why not?

? How many more houses

would I need to share six

people equally (if there

were four houses to start

with)?

? There are 11 people and four houses.

There are five people in one house and

three in another. How many people might

the other houses have? Have you found

all possibilities? How do you know?

Activity overview In this activity children explore sharing people between houses. Allow your child opportunities to

explore equal and unequal grouping. Explore zero as a set and what it would mean to have zero people in a house.

Children can begin to make connections between the number of houses and the number of people, for example, multiples

- six people can be shared equally between three houses but not four.

Resources: Countable objects to represent people e.g. figures, cubes, counters. Rows (of various sizes) of paper houses

(included)

Suggested sentence structures:

“There are __ people in each house.”

“I would need __ more/fewer people to have the

same number in each house.”

“There cannot be the same number of people in each house because...”




Activity 3: Target

Key learning: To apply knowledge of addition, subtraction and doubles

Key vocabulary:

Number names 0-10, add, subtract, plus,

minus, double, exactly

Important aspects to draw attention to and possible modifications:

Before rolling the die, encourage your child to think about what number they would like to

land on and why. What number do they not want to land on? Why?

The target number of ten can be increased/decreased to allow more focused attention on the preferred

numbers to win.

Vary the resources: they could complete the activity using a bead string, counters, pictorial representations,

abstract, etc.

Encourage to think more than one step ahead about what numbers they would like to roll, for example, a

five and a five; or a five, three and two, etc.


used.

Likely misconceptions/potential difficulties related to this learning:

Some children may find it challenging to think one/two steps ahead about what numbers they might need

and might just play the game one step at a time. Repeating the activity several times, should encourage

more pattern seeking.

Some children may struggle to remember what number of cubes they have and may have to recount them

each time. Encourage your child to count on from the number they have rather than count all.


? You have seven cubes now,

what number do you want to

roll to win the game? What

number do you not want to

roll?

? Does it make a difference who

has the first turn? How do you

know?

? What is the least number of

turns you could have to win the

game?

Activity overview This is a two player activity. Roll a one to six sided die. They then count out this number of cubes and

place them onto a ten frame. Continue to take turns until one person has ten cubes. They must land on a number that will

give them exactly ten cubes.

Alternatively, begin with ten cubes and subtract the number that they select. The winner is the first person to have zero

cubes. Once children are familiar, introduce a ‘magic number’ which can be doubled.

Resources: A die, cubes (or replace with any countable objects), ten frame (included)


“I want to roll a __ because that will get me closer to ten.”

“I do not want to roll a five because I will then have more than ten.”

“I need to count out four cubes because double two is four.”




Activity 4: Maths Trail

Key learning: To apply knowledge of number, shape and measures in their surrounding

environment

Key vocabulary:

Number names, shapes, size,

big, small, round, tall, short, more, fewer,

etc.


Aspects to draw attention to will depend on the setting in which you complete the trail. Encourage your

child to find the maths around them - it is everywhere; ask questions such as; how many,

are there more __ or ____; how do you know? Look at that plant and the leaves - what

maths can you see there?

If there is passing traffic near your home, how many red cars pass in one minute? Model how to record

using a tally to help your child count them.

Explore the registration plates on the cars, what numbers can they see? Is there a pattern between some/

any of the number plates?

Look for tessellations and patterns in footpaths/walls/etc. How many of each shape do they see? What

shapes are they? How many hops would they need to hop on each stone or to get to the end of the path?

Allow your child to explain their own thinking to allow connections to be made between this and their knowledge of

maths.


Some children may find it challenging to spot the maths around them. Think carefully about the

small groups in which they are placed to support them in this.

Children may not see shape/patterns/size as being part of maths and may find it challenging to

find the maths in natural objects, such as a tree, plant, etc. Have discussion around these


? Look at these three plants.

Which is the odd one out and

why?

? Find as many links as you can to

the number nine. What is the

same and what is different

about them?

? What is the longest line you can

find? How could you measure

how long it is?

Activity overview Explore your surrounding environment with your child. Children should not be limited to finding just

numbers in their surrounding environment but shape and measures as well. Suggested prompts have been given below

but these will need to be adapted to suit your home/garden. Afterwards, have a sharing session to discuss what they have

found.


“I can see the number __ on the _____.”

“I can count __ trees. Some are taller than the school.”

“I can wrap my arms around this tree trunk - it is not very thick. We need

two children to ‘hug’ this tree though. The trunk is very thick.”




Activity 5: Waterspouts and Spider silk

Key learning: To practise counting forwards and backwards from a number

Key vocabulary:

Number names 0-20, forwards, backwards,

on, back


Counting on from the number they are currently on and relating that to addition, for

example, rolling a four when on 11: 1, 2, 3, 4. 11 plus four is equal to 15.

Ask your child to think one/two steps ahead - what number would they like to land on?

Why? What would you need to roll to land on that space?

If a player is ahead or behind their opponent, how many steps would you need to pass the other player?

Can you do this in one turn/two turns? How do you know?

Ask your child about the number of steps you can take when you land on a drainpipe or spider silk. Will you

always win if you land on a drainpipe?

Allow your child to explain their own thinking to allow connections to be made between this and the

representations used.


Some children may find it challenging to think one/two steps ahead when playing. Focus on one

step at a time with them. Recording the moves they make may help them to see patterns more

clearly.

Some children may not connect that as they move on the board the numbers are increasing

and as they fall down the spider silk the numbers are decreasing.


? What number would you like to

land on next? Why? What

would you need to roll to land

on that number?

? In how many moves can you

win the game? What numbers

would you need to roll to do

so? Will you land on any drain-

pipes or spider silks with these

numbers?

? What other rules could you add

to the spaces, for example, go

forward one/two spaces?

Which numbers would you

place these rules on? Why?

Activity overview Play a version of the traditional game of Snakes and Ladders. It is recommended that die with spots

(rather than die with numbers) are used so children are developing their subitising skills as they play. In this game,

children can climb up the water spout and slip down spider silk.

Resources: a die, waterspouts and spider silk board (included)


“I have rolled at three; one, two, three, I have landed on the number

nine.”

“I have landed on a spider silk - I need to go back to space number one.”




Activity 6: Make ten

Key learning: To explore different ways of making ten

Key vocabulary:

Number names 0-10, make ten, add, plus, is

equal to


Encourage them to work systematically - have they found all the possible pairings using their cards? Can they order

them?

Are there any pairings they could make that are not on the cards?

Can you find all possible pairings for ten - how do you know you have found them all?

Draw their attention to commutativity - is 1 + 9 = 10 the same as 9 + 1 = 10? Why/why not?

When your child can no longer make a pairing, then have them take one card from their partner’s hand to see if

that makes the desired number.


used.


Some children may still count all when pairing the cards. Encourage them to count on from the

card with the greatest number.

Some children may find it challenging to recognise commutativity. Using concrete resources

such as bead strings, cubes, a ten frame, should show them more clearly that they are the

same.


? Does it matter which way I add

the cards? Will I still have ten?

How do you know?

? Have you found all pairings to

ten? How do you know? Are

there more pairings to ten?

What about pairings to nine?

Can you see a pattern?

? Could you use three cards to

make ten? How many different

pairings of three cards can you

make?

Activity overview

Place the number/dotted cards face up on the table. Take it in turns to select two cards which must pair together to make

ten. If the cards do not make ten, they must place both back on the table. They can place a dotted card with a number

and/or two dotted cards together or two number cards together. This activity can be repeated using a different total

number so that your child can practice their number bonds to and within ten.

Resources: Number and dotted cards (included)


“Five dots add five dots is equal to ten dots.”

“I have three dots and the number nine. That is not equal to ten.”




Activity 7: Number patterns

Key learning: To recognise and extend a pattern

Key vocabulary:

Number names 0-15, pattern, bigger,

smaller, one more, above, below


Ask your child to describe the relationship between each row. They may recognise that pyramid two has

three more cubes that pyramid one, pyramid three will have four more cubes than pyramid

three, etc. How many more cubes will the next pyramid have?

Can they spot a relationship between the total number of cubes in each pyramid? What

might the total number of cubes be in the next pyramid? They may recognise that they will need to add the

bottom row plus one to find the next total, for example, pyramid two has six cubes and there are three cubes

in the bottom row. The next pyramid will have four cubes in the bottom row: 6 + 4 = 10. The next pyramid

will have ten cubes.

Share different methods that you may have for extending the pattern, for example, you may add one cube

to each row rather than adding on a bottom row. Are there any other ways?

You could be given the first four or five pyramids in the pattern and just asked to talk about

what they notice. What’s the same and what’s different?

Allow your child to explain their own thinking to allow connections to be made between this and the

representations used.


Some children may find it challenging to spot the pattern and just see the pyramid as ‘getting

bigger’. Model for your child how the number of cubes in each pyramid is increasing or each pyramid could

be laid on top of the next pyramid to show that it has an extra bottom row.


? What’s the same and what’s

different?

? What might come before the

first pyramid? What would

come next? Can you show me

what the 7th one would be?

? Which one is the odd one out?

Why?

Activity overview

Children use the template attached and place cubes on each square in the first pyramid. They can then repeat this for the

second pyramid. Your child must then decide what the third and fourth pyramid would look like. Create the pyramids and

articulate how it is changing.

Resources pyramid template (included) , cubes (or other countable small objects.)


“This pyramid has three fewer cubes.”

“We are adding one row each time to the bottom of the pyramid. The

bottom row has one more cube than the row above it.”


Activity 1—Take down the wall

Activity 1 —Take down the wall

Activity 2— Equal and unequal sharing

Activity 2— Equal and unequal sharing

Activity 3 — Ten frames

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Mo

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20

1

9

18

1

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16

11

1

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13

1

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15

10

9

8

7

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1

2

3

4

5

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Fin

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Activity 5 — Waterspouts and Spider silks

1 one

2 two

3 three

4 four

5 five

6 six

Activity 6 — Make 10

7 seven

8 eight

9 nine

10 ten

0 zero

Activity 6 — Make 10

Documents

At home materials Reception Weeks 7—10 Depth of numbers ... · Reception Weeks 7—10 Depth of numbers within 20 Using the at home materials This pack contains seven activities